Algebraic isomonodromic deformations and the mapping class group
| Autor: | Gaël Cousin, Viktoria Heu |
|---|---|
| Přispěvatelé: | Laboratoire Angevin de Recherche en Mathématiques (LAREMA), Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), ANR, Labex IRMIA, ANR-13-JS01-0002,Iso-Galois,Déformations iso-galoisiennes de feuilletages holomorphes(2013), ANR-13-BS01-0001,Vargen,Variétés de caractères et généralisations(2013), Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
14D05 14F35 20F36 34M56 Rank (linear algebra) Mathematics - Complex Variables General Mathematics 010102 general mathematics 16. Peace & justice 01 natural sciences Mapping class group Connection (mathematics) Mathematics - Algebraic Geometry Mathematics - Geometric Topology Monodromy Genus (mathematics) 14D05 14F35 20F36 34M56 0103 physical sciences [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 010307 mathematical physics Isomonodromic deformation 0101 mathematics Orbit (control theory) Algebraic number Mathematics |
| Popis: | The germ of the universal isomonodromic deformation of a logarithmic connection on a stable n-pointed genus g curve always exists in the analytic category. The first part of this paper investigates under which conditions it is the analytic germification of an algebraic isomonodromic deformation. Up to some minor technical conditions, this turns out to be the case if and only if the monodromy of the connection has finite orbit under the action of the mapping class group. The second part of this paper studies the dynamics of this action in the particular case of reducible rank 2 representations and genus g > 0, allowing to classify all finite orbits. Both of these results extend recent ones concerning the genus 0 case. Comment: Final version, 39 pages. To appear in Journal de l'Institut de Math\'ematiques de Jussieu |
| Databáze: | OpenAIRE |
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